The topology of a semisimple Lie group is essentially unique |
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Authors: | Linus Kramer |
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Affiliation: | Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany |
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Abstract: | We study locally compact group topologies on simple and semisimple Lie groups. We show that the Lie group topology on such a group S is very rigid: every “abstract” isomorphism between S and a locally compact and σ-compact group Γ is automatically a homeomorphism, provided that S is absolutely simple. If S is complex, then noncontinuous field automorphisms of the complex numbers have to be considered, but that is all. We obtain similar results for semisimple groups. |
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Keywords: | Lie group Locally compact group Continuity of homomorphisms |
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